My guess is that it might depend on what you mean by bias and what you mean by empirical Bayes. A lot of empirical Bayes does not deal with uncertainty in the nuisance parameters. That being so it is clear that if you proceed to calculate frequentist confidence intervals these do not have the correct coverage. A discussion with theoretical arguments and some simulations was given by me in Various, Varying, Variances http://www.ncbi.nlm.nih.gov/pubmed/24492794 It is also clear that the shrinkage weights will not be 'optimal'. Whether this is a bias or not depend on your point of view.

The books by Cox and Solomon https://www.crcpress.com/Components-of-Variance/Cox-Solomon/p/book/9781584883548

and Carlin and Louis

 http://link.springer.com/article/10.1023%2FA%3A1018577817064

would be worth looking at. Otherwise try the meta-analysis literature Viechtbauer, Rücker, Lumley are likely suspects..

It's pretty much the same problem as REML has so Kenward and Roger 1997 and citations to it is also a good place to look.

Dear Stephen,

many thanks for the prompt and comprehensive reply. I will have a close look at the recommended literature.

Gerd

You are welcome. I would be interested to know in due course what you discover.